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Full text of "Mathematical And Physical Papers - Iii"

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incident vibrations of the ether agitate the sensitive molecule or complex molecule, and this agitation gradually spreads outwards by the molecular forces into the complex system formed of the surrounding molecules and molecular groups, which may be mostly themselves insensible, very much in the manner in which if a very minute portion of a metallic mass be supposed strongly heated to start with, the heat is rapidly diffused into the neighbourhood by conduction ; and if the heated spot is at the surface, so as to permit of radiation outwards, the radiant heat is of a mean rcfnmgibility which decreases as the time goes on. Indeed the phenomenon of fluorescence, which is a brief phosphorescence, seems to be; closely akin to the very familiar one of the heating of a body by sunshine, and the consequent emission of heat-rays of low refrangibility.
Being desirous of seeking an analogy in some simple dynamical problem which could be actually worked out, I took the case of an infinite weightless flexible and inextensible stretched string, loaded at equal intervals with equal masses, and supposed one of the masses permanently acted on by a small transverse disturbing force expressed by cs'mnt, t being the time, and I demanded the permanent state of motion of the masses. It proved to be of a different character according as the frequency of the disturbing force was greater or less than that corresponding to the shortest of the periods, infinite in number, belonging to the natural oscillations of the loaded string when no disturbing force is acting. 'Fake the mean position of the mass on which the disturbing force acts for the origin of abscissae. The motion will of course be symmetrical on the two sides of the origin, and it will suffice to refer to that on the positive side. When the period of the force is greater than the critical period, the disturbance extends to infinity. It is of the nature of an undulation propagated outwards from the origin, and the various masses will at any moment lie on a curve of wines. But when the period of the force is less than the critical period, the disturbance instead of extending to infinity deereases on receding from the origin, and the masses at any moment lie in a curve derived from a fixed curve of sines by diminishing at a given moment the ordinates in geometric progression as we recede from the origin, while as the time changes all the ordinates vary as sin nt.